Abstracts

An epidemiologist's life on the edge (of the science-policy interface)

Ebola, MERS, pandemic influenza and SARS have all posed serious threats to our health and economic wellbeing in recent years. In each of these cases, statistical (and more broadly mathematical) epidemiologists contributed to top-level policy discussions of diseases control policy development, implementation and contingency planning. The methods build upon foundations of epidemiological modelling and analysis of both human and animal diseases (HIV/AIDS, BSE, vCJD and foot-and-mouth disease, among others). The potential impact of such analyses is enormous, but it can be challenging to provide robust answers to key scientific and policy questions. In the midst of an epidemic response effort, it really does feel like living on the edge.

We all like to think of ourselves as strong, independent and single-minded individuals. But despite our illusion of free will, most of the time we find ourselves swept along by the actions of those around us. These hidden connections affect everything from the movement of crowds to fashions and memes, and can be used to understand the mathematics of friendships and even catch the odd burglar or two. Hannah takes you on a whistle stop tour of how the patterns in how we are connected make us surprisingly predictable - as long as you know a little bit of mathematics, that is.

Epidemics of infectious disease remain one of the biggest threats to humankind. Here we will look at some of the mathematics used to help us understand disease, from learning how an individual virus particle works through to designing vaccination strategies. We will see that many problems can be tackled using school mathematics ... with a bit of creativity.

This talk will give an overview of the history of various hard problems in number theory which are used as the basis for cryptosystems. I will survey the evolution of attacks on them and improvements to the algorithms which enabled these attacks. Then I will present some current proposals for post-quantum systems using lattice-based cryptosystems in cyclotomic number fields and give the ideas behind some recent attacks.

The data scientists who use maths to find useful patterns in large data sets have been described as the new rock stars of the technology world. One particularly promising application area for big data analysis is computer network security. Miranda will talk about some general issues with analyzing big data to discover security problems in enterprise computer networks, and some specific techniques that have been successful.

Prime numbers are fundamentally important in mathematics. Join Vicky to discover some of the beautiful properties of prime numbers, and learn about some of the unsolved problems that mathematicians are working on today.

In 2014, Maryam Mirzakhani of Stanford University became the first woman to be awarded the Fields medal. The starting point of her work was a remarkable relationship called McShane's identity, about the lengths of simple closed curves on certain hyperbolic surfaces. The proof of this identity, including the Birman-Series theorem about simple curves on surfaces, uses only quite basic ideas in hyperbolic geometry which I will try to explain. We will then look briefly at Mirzakhani's ingenious way of exploiting the identity and where it led.

In this presentation, I will show you how applied mathematics plays an important role in the understanding of our natural environment. My research expertise covers granular materials and I have traveled to various places on this earth to investigate the behavior of snow avalanches in mountains and sand dunes in deserts. Our research group combines field experiments with laboratory experiments (in the GK Batchelor laboratory underneath the courtyard of the Centre for Mathematical Sciences in Cambridge) and uses mathematical tools to model these observations. Our goal is to understand the dynamic behavior of granular flows and potentially even predict some outcomes of avalanches.